We used Pythia8 version 8.235 throughout this study with the most recent Monash [1]} tune is used as baseline for the parameter optimisation. We use Professor v2.2 [2]} to perform the tuning and Rivet v2.5.4 [3]} for the implementation of the measurements. In Professor, a method permits to make simultaneous optimisation of several parameters by using analytical approximations of the dependence of the MC response on the model parameters (this idea was introduced first in Ref. [4]}). In order to minimises the differences between the interpolated functions and the true MC response, we use a fourth-order polynomial. The values of the model parameters at the minimum are then obtained with a standard \(\chi ^2\)  minimisation of the analytic approximation to the corresponding data using Minuit [5]}. In this work, we tuned the \(a\)  and \(b\)  parameters of the Lund fragmentation function (\(a\)  and \(<z_\rho >\)  in the new parametrization) and the \(\sigma \)  parameter which governs the transverse components (see e.g. [6]}). The default values of the parameters and their allowed range in Pythia8 are shown in Table REF .
